Math 1530
Solutions to Homework 1
September 6, 2011
Chapter 1 Number 1
Suppose that x + r is rational. Since the rational numbers form a eld, it follows
that x = (x + r) r is rational, contrary to hyp
Background:
T he problem is what are the best specifications for tin cans? Assume that the cans
will be made from tin sold in rolls of 2 meter width and 10 meter length. In reality lots
of food/drinks
CS 1520 / CoE 1520: Programming Languages for Web Applications (Spring 2013)
Department of Computer Science, University of Pittsburgh
Assignment #3: Javascript
Due: 11:59pm, Friday, April 19th, 2013
R
CS 1520 / CoE 1520: Programming Languages for Web Applications (Spring 2013)
Department of Computer Science, University of Pittsburgh
Term Project: Pittsburgh Interactive Research Accounting System (p
CS 1520 / CoE 1520: Programming Languages for Web Applications (Spring 2013)
Department of Computer Science, University of Pittsburgh
Assignment #1: Perl
Due: 11:59pm, Friday, February 15th, 2013
Rele
ADVANCED CALCULUS I FOR UNDERGRADUATE STUDENTS
(MATH 1530)
HOMEWORK NO. 3
INSTRUCTOR & TEACHING ASSISTANT: GEORGE SPARLING & CEZAR LUPU
Problem 1. Decide which of the following sets is compact. For th
ADVANCED CALCULUS I FOR UNDERGRADUATE STUDENTS
(MATH 1530)
HOMEWORK NO. 4
INSTRUCTOR & TEACHING ASSISTANT: GEORGE SPARLING & CEZAR LUPU
Problem 1. (i) Show that ex x + 1 for each x R, with equality if
ADVANCED CALCULUS I FOR UNDERGRADUATE STUDENTS
(MATH 1530)
HOMEWORK NO. 5
INSTRUCTOR & TEACHING ASSISTANT: GEORGE SPARLING & CEZAR LUPU
Problem 1. Let p be a real number, p 6= 1. Compute
1p + 2p + . .
Advanced Calculus, Exam 2, 11/21/14
Name:
Twenty points per question.
The best six questions will count.
Question 1
For n a fixed positive integer, put f (x) = xn , for any non-negative x.
Using appro
Solutions Homework, MATH 414, Fall 2010
Chapter 1, 12:) (a) Suppose there is no s [b , b] S. Then b < b is
an upper bound for S contradicting the assumption b = l.u.b.S.
(b) No. For example consider S
Advanced Calculus, Exam 1, 10 /'14_/ 14
Name:
Show your work.
Twenty points per question.
The best ve questions will count.
Question 1
For each of the following statements, either prove or disprove it
Advanced Calculus,
Final Exam, 12/13/14
Name:
The best six questions will count, 20 points per question
Question 1
'Iiue/false: give your reasons.
c There is an uncountable subset of the reais without
Background:
The problem is what are the best specifications for tin cans? Assume that
the cans will be made from tin sold in rolls of 2 meter width and 10 meter
length. In reality lots of food/drinks
1. FOREST (Forest_No, Name, Area, Acid_Level, MBR_XMin, MBR_XMax,
MBR_YMin, MBR_YMax)
PK
(Forest_No);
UQ
(Name);
No FKs;
Assumptions: Each forest has a unique ID and a unique name.
Although unlikely,
1. FOREST (Forest_No, Nam e, Area, Acid_Level, MBR_XMin, MBR_XMax,
MBR_YMin, MBR_YMax)
PK
(Forest_No);
UQ
(Name);
No FKs;
Assumptions: Each forest has a unique ID and a unique name.
Although unlikely,
Math 1530
Solutions to Homework 2
September 26, 2011
Chapter 1 Number 8
Let F be any ordered eld, and let a F with a = 0. Then either a > 0 or
a > 0. Since the product of positive elements is positive
Math 1530
Solutions to Homework 3
October 7, 2011
Chapter 2 Number 19
(a) Since A and B are closed, A = A and B = B , so
A B = A B = A B = .
(b) Let A and B be disjoint open sets. For any p A there is
Math 1530
Solutions to Homework 4
October 25, 2011
Chapter 3 Number 3
We rst show that sn < 2 for every n N, by induction. The case n = 1 is
clear. Let n N, and suppose that sn < 2. Then
sn+1 =
2+
sn
Math 1530
Solutions to Homework 5
November 5, 2011
Chapter 3 Number 8
Since
an bn converges if and only if
an (bn ) converges, there is no loss
in assuming that (bn ) is decreasing. Since (bn ) is mon
Math 1530
Solutions to Homework 6
November 21, 2011
Chapter 4 Number 6
First, assume f is continuous. Dene F : E R2 by F (t) = (t, f (t). Then F
is continuous, and E is compact, so F (E ) is compact.
Math 1530
Solutions to Homework 7
December 5, 2011
Chapter 7 Number 15
The function f must be constant on [0, ). Let > 0. By equicontinuity, there
is a > 0 such that for all x [0, 1] with x < and all
Math 1530
Topics for the Midterm Exam
Denitions
Supremum and inmum
Norm
Euclidean norm
Metric
Open set
Closed set
Interior point
Boundary point
Limit point
Closure
Continuous function
Limit of a seque
Math 1530 Midterm Exam
October 17, 2011
Name:
Instructions: No books or notes may be used during the exam. Attempt all problems, giving complete and clear explanations of your answers.
1. (5 points ea
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